She was literally squaring it with herself (without success) as she was doing it and she still didnt hesitate. or even attempt to save him.
Now I think about it what she did wasn't a cold blooded murder at all, it was as hot as hot could be and I am not talking about a crime of passion, that was something else altogether.
Maddox was a dead man before he even boarded that ship, he had no defence against her and would never ever suspect her.
Surely the Commodore would realise that she will spill the beans now that it is done, unless we are supposed to believe that no one will suspect her after he just happens to die, that would be ridiculous.
Does the Commodore want Picard to find out indirectly.